# On the Turnpike Property and the Receding-Horizon Method for Linear-Quadratic Optimal Control Problems

arXiv: https://arxiv.org/abs/1811.02421 · HTML: https://mlsanity.com/paper/1811.02421/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2018.

## Built on by (most cited first, 1 of 1)

- [Horizon-Uniform Sensitivity and Decay of Terminal Reward Perturbations in Discrete-Time Pontryagin Systems](https://mlsanity.com/paper/2606.17762/) (2026)

## Abstract (arXiv)

Optimal control problems with a very large time horizon can be tackled with the Receding Horizon Control (RHC) method, which consists in solving a sequence of optimal control problems with small prediction horizon. The main result of this article is the proof of the exponential convergence (with respect to the prediction horizon) of the control generated by the RHC method towards the exact solution of the problem. The result is established for a class of infinite-dimensional linear-quadratic optimal control problems with time-independent dynamics and integral cost. Such problems satisfy the turnpike property: the optimal trajectory remains most of the time very close to the solution to the associated static optimization problem. Specific terminal cost functions, derived from the Lagrange multiplier associated with the static optimization problem, are employed in the implementation of the RHC method.